The present invention relates to a method for improving the archiving of a curve plotted from N measured experimental values of a dynamic parameter of a viscoelastic material where this parameter is a function of the deformation.
Among the properties of viscoelastic materials, those most closely related to their use are the dynamic properties, in other words the responses to the application of deformations.
In order to be able to select, at the moment of use, the material which best meets the final dynamic requirements of a desired product, it is necessary to know the dynamic properties of a large number of materials, and consequently to have made numerous experimental measurements beforehand for the purpose of characterizing them.
For example, in order to determine the dynamic properties of such materials, experimental measurements of the strain are generally made after cycles of deformation. These dynamic properties, however, depend on the temperature and frequency of their measurement. Moreover, for some materials, such as polymers filled with reinforcing materials, or asphalts, the situation is even more complex, since the properties also depend on the applied deformation. Consequently, the characterization of each material requires the acquisition of a large number of experimental values for a variety of temperature, frequency of use and applied deformation, and, subsequently, the archiving of the values thus obtained or of the graphs showing the curves passing through these experimental values. This storage requires long periods of time and paper or data-processing archives which are very large and easily damaged.
The inventors of the present invention, therefore, tackled the problem of simplifying the process of archiving the acquired experimental values of a dynamic parameter of a viscoelastic material where this parameter is a function of the deformation.
More precisely, in the case of the experimental curve, at a given temperature, of any dynamic parameter P as a function of any deformation q applied to a generic test specimen of a viscoelastic material, the inventors of the present invention unexpectedly discovered that this experimental curve could be reduced to a summation of exponentials of the type       P    ⁡          (      q      )        =            P      0        +                  ∑                  i          =          1                ∞            ⁢              xe2x80x83            ⁢                        P          i                ⁢                  ⅇ                      -                          q                              q                i                                                        
where
P(q) is the value of the dynamic parameter as a function of the deformation q;
P0 is the value of the dynamic parameter at infinite deformation;
q is the deformation in question;
Pi is the value of the characteristic dynamic parameter of the i-th deformation;
qi is the characteristic deformation at which the i-th exponential intervenes.
The inventors also realized that 5 values, namely P0, P1, q1, P2, q2, were sufficient to provide a good approximation of the said experimental curve.
For example, in the case of the experimental curve of the modulus of elasticity Gxe2x80x2 as a function, at a given temperature, of a torsion xcex3 applied to a cylindrical test specimen consisting of a mix, filled with lampblack, for a tire tread, the inventors found that this experimental curve could be reduced, according to the present invention, to the relation             G      xe2x80x2        ⁡          (      γ      )        =            G      0      xe2x80x2        +                  G        1        xe2x80x2            ⁢              ⅇ                  -                      γ                          γ              1                                            +                  G        2        xe2x80x2            ⁢              ⅇ                  -                      γ                          γ              2                                          
Finally, when they also investigated the experimental curves of the complex modulus G*, of the viscous modulus Gxe2x80x3 (where |G*|={square root over ((Gxe2x80x2)2+L +(Gxe2x80x3)2+L )}), and of the loss factor tanxcex4 (where tanxcex4=Gxe2x80x3/Gxe2x80x2) as a function of the torsion xcex3 applied to the test specimen, the inventors unexpectedly discovered that these could also be represented by the aforesaid summation of exponentials, and that five corresponding values, as shown above, were sufficient to provide a good approximation to each of the aforesaid experimental curves.
A first aspect of the present invention is therefore a method for improving the archiving of a curve plotted from at least N (Nxe2x89xa75) measured experimental values of a dynamic parameter P of a viscoelastic material where this parameter is a function of the deformation q at a given temperature, characterized in that it comprises the following stages:
a) the acquisition of N experimental measurements of the said dynamic parameter P of the said viscoelastic material where this parameter is a function of the deformation q at a predetermined temperature;
b) the determination, by successive approximations, of the values P0, P1, q1, P2, q2, which, when inserted in the relation                               P          ⁡                      (            q            )                          =                              P            0                    +                                    P              1                        ⁢                          ⅇ                              -                                  q                                      q                    1                                                                                +                                    P              2                        ⁢                          ⅇ                              -                                  q                                      q                    2                                                                                                          (        A        )            
xe2x80x83generate the curve which best approximates the experimental curve passing through all the points which represent the N values determined experimentally during the preceding stage a);
c) the archiving of the values P0, P1, q1, P2, q2 found in this way.